An Observer-Based Robust Adaptive Fuzzy Back-Stepping Control of Ball and Beam System

Abstract

In this paper, an observer-based robust adaptive fuzzy back-stepping control is provided for a ball and beam system while accessible state variables of the system are position and angle of the ball and beam, respectively. Firstly, based on the mentioned measureable signals, a velocity observer is employed to estimate rate of the available states of the system and then a robust adaptive fuzzy back-stepping control is accomplished by the estimated states of the system. Asymptotic stability of the observer-based control system in the presence of un-modeled dynamics and uncertainties is shown by Lyapunov theory. Simulation results illustrate proper functioning of the adaptive fuzzy back-stepping control method on the ball and beam system. Also, the results of the proposed method are compared with an existing method in order to show performance and accuracy of the controller.